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General Physics II Electrostatic: Principles & Applications

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Electric charge • The early Greeks knew that if a piece of amber was rubbed, it would attract bits of straw. This is an early example of electrostatics. The English word,electron,is derived from the Greek work for amber. • The ancient Greeks also knew that a certain type of rock, called lodestone, would attract iron and always keep the same orientation if hung from a string and left free to rotate. This is an early example of magnetism. • But only in the 19th century did scientists realize that electrostatics and magnetism were both part of the same phenomena which we call electromagnetism. • James Clerk Maxwell took the ideas of Michael Faraday and some of his original discoveries and put them into mathematical form around the middle of the 19th century. We now know these laws as Maxwell's Equations

Conductor and insulator • Conductors are materials in which the electrons can move rather freely (i.e. they readily conduct a flow of electrons). • Non-conductors or Insulators are materials in which the electrons are more tightly bound to the atoms and generally are not free to move. • Examples of conductors are metals such as copper, silver, Aluminum plus salt water solutions (the human body falls into this category). • Examples of insulators are wood, plastic, stone; in short, any non-metal. • The earth acts as a large conductor and has a very large capacity to absorb charge concentrations from smaller conductors. • So any charge on a conductor will be lost if there is a path to ground.

Substances that fall between the metals and the insulators are called semiconductors. • Semiconductors such as Silicon and Germanium are widely used in modern electronics since their properties may be radically altered by the addition of small amounts of impurity atoms. • Superconductors are perfect conductors in the sense that they offer no resistance to the flow of charges.

Positive and negative charge • Like charge repel one another and unlike charges attract one another where a suspended rubber rod is negatively charged is attracted to the glass rod. But another negatively charged rubber rod will repel the suspended rubber rod.

Charge is Conserved • Electric charge is conserved. The net charge of an isolated system may be positive, negative or neutral. Charge can move between objects in the system, but the net charge of the system remains unchanged.

Charge is Quantized • In the early part of the 20th century Robert Millikan performed an experiment to determine the smallest possible charge in nature. • Millikan found that that basic charge is 1.6x10-19 Coulombs. • This was later found to be the charge on every proton and electron (negative for electrons). • Every experiment since then has observed the basic electron charge or some integral multiple of it.

Coulomb’s Law The electrostatic force of a charged particle exerts on another is proportional to the product of the charges and inversely proportional to the square of the distance between them.

where K is the coulomb constant = 9  109 N.m2/C2. • The above equation is called Coulomb’s law, which is used to calculate the force between electric charges. In that equation F is measured in Newton (N), q is measured in unit of coulomb (C) and r in meter (m).

Multiple Charges in One Dimension Things get a bit more interesting when you start to consider questions that have more than two charges. • In the following example you have three charges lined up and are asked to calculate the net force acting on one of them. • Do one step at a time, and then combine the answers at the end.

Example 3 The following three charges are arranged as shown. Determine the net force acting on the charge on the far right (q3 = charge 3).

Step 1: Calculate the force that charge 1 exerts on charge 3... • It does NOT matter that there is another charge in between these two… ignore it! It will not effect the calculations that we are doing for these two. Notice that the total distance between charge 1 and 3 is 3.1 m , since we need to add 1.4 m and 1.7 m .

The negative sign just tells us the charges are opposite, so the force is attractive. Charge 1 is pulling charge 3 to the left, and vice versa. Do not automatically treat a negative answer as meaning “to the left” in this formula!!! Since all I care about is what is happening to charge 3, • all I really need to know from this is that charge 3 feels a pull towards the left of 4.9e-2 N.

Step 2: Calculate the force that charge 2 exerts on charge 3... • Same thing as above, only now we are dealing with two negative charges, so the force will be repulsive. • The positive sign tells you that the charges are either both negative or both positive, so the force is repulsive. I know that charge 2 is pushing charge 3 to the right with a force of 2.5e-1 N. • Step 3: Add you values to find the net force.

Equilibrium • Example Two fixed charges, 1C and -3C are separated by 10cm as shown in figure below (a) where may a third charge be located so that no force acts on it? (b) is the equilibrium stable or unstable for the third charge?

Example • Two charges are located on the positive x-axis of a coordinate system, as shown in figure below. Charge q1=2nC is 2cm from the origin, and charge q2=-3nC is 4cm from the origin. What is the total force exerted by these two charges on a charge q3=5nC located at the origin?

Problems • Two protons in a molecule are separated by a distance of 3.810-10m. Find the electrostatic force exerted by one proton on the other. • A 6.7C charge is located 5m from a -8.4C charge. Find the electrostatic force exerted by one on the other. • Two fixed charges, +1.010-6C and -3.010-6C, are 10cm apart. (a) Where may a third charge be located so that no force acts on it? (b) Is the equilibrium of this third charge stable or unstable? • A 1.3C charge is located on the x-axis at x=-0.5m, 3.2C charge is located on the x-axis at x=1.5m, and 2.5C charge is located at the origin. Find the net force on the 2.5C charge.

A point charge q1= -4.3C is located on the y-axis at y=0.18m, a charge q2=1.6C is located at the origin, and a charge q3=3.7C is located on the x-axis at x=-0.18m. Find the resultant force on the charge q1. Three point charges of 2C, 7C, and –4C are located at the corners of an equilateral triangle as shown in the figure 2.9. Calculate the net electric force on 7C charge. Two free point charges +q and +4q are a distance 1cm apart. A third charge is so placed that the entire system is in equilibrium. Find the location, magnitude and sign of the third charge. Is the equilibrium stable?

Four point charges are situated at the corners of a square of sides a as shown in the figure 2.10. Find the resultant force on the positive charge +q. • Three point charges lie along the y-axis. A charge q1=-9C is at y=6.0m, and a charge q2=-8C is at y=-4.0m. Where must a third positive charge, q3, be placed such that the resultant force on it is zero? • A charge q1 of +3.4C is located at x=+2m, y=+2m and a second charge q2=+2.7C is located at x=-4m, y=-4m. Where must a third charge (q3>0) be placed such that the resultant force on q3 will be zero?

The Electric Field • Definition of the electric field (E) • Calculating E due to a charged particle • To find E for a group of point charge • Electric field lines • Motion of charge particles in a uniform electric field • The electric dipole in electric field